Britain's economic mix of a big banking sector and low level of benefits leaves the country vulnerable to sharply rising inequality unless it moves rapidly to a "fairer" system of redistributing tax burdens and social opportunities, according to an OECD report.

The thinktank, which last month warned that income inequality among working-age people had risen faster in Britain since the mid-1970s than in any other rich nation – said in a review of 30 years of data on economic crises that economies with big financial sectors amplified the chances of societies becoming more unequal.

The OECD said this effect would be mitigated by generous unemployment benefits, but this "social protection" was unavailable in Britain.

"Britain will see an increase in its inequality in this period unless it acts quickly to spread risks more fairly," said Isabelle Journard, senior economist with the thinktank.

In a series of chapters for the forthcoming publication Going for Growth, Journard outlined Britain's weaknesses. Almost one in five of people aged between 25 and 34 do not have five good GCSEs (or their equivalent), and academic performance is dramatically affected by parental performance, much more so than in other comparable rich nations.

Another issue, said Journard, was that 40% of women were in part-time employment – 15% higher than average among rich nations – which was "almost certainly" related to the fact the UK had some of the highest childcare costs, equivalent to more than 45% of the average wage.

The OECD called for education spending to be better targeted so the poor benefited more from proposed reforms. "The pupil premium is a good idea but we still feel that it could do more to benefit disadvantaged students," it said.

It also called for a shakeup of the way housing is taxed, questioning why house sales did not attract capital gains tax. "UK housing taxation appears to favour wealthier and older households relative to poorer and younger ones. We have seen from America, where this is a big driver of inequality because those who own homes are richer and they do not pay tax on the profit when they sell their homes. This would help to reduce inequality in the coming years," said Journard's colleague Romain Duval.

Duval said Britain's council tax regime was "highly regressive" and needed reform. "In England, the tax liability for properties over £320,000 is only twice the liability for properties of £70,000 and three times the liability for houses under £40,000. Low-income households are entitled to a council tax benefit. However, the takeup is only around 65%."

Duval said the OECD advocated a replacement with "a property tax based on current market values or a land tax".